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Find the number of solutions of $cos x=fraclvert x rvert80$
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Find the number of solution of $cos x=fraclvert x rvert80$
Domain of $x$ is $[0,pi]$ and the range of $x$ is $[-80,80]$. I am not able to proceed.
trigonometry
edited Jul 24 at 6:59
Gibbs
3,3631524
asked Jul 24 at 4:36
Samar Imam Zaidi
1,063316
add a comment |Â
up vote
0
down vote
favorite
Find the number of solution of $cos x=fraclvert x rvert80$
Domain of $x$ is $[0,pi]$ and the range of $x$ is $[-80,80]$. I am not able to proceed.
trigonometry
edited Jul 24 at 6:59
Gibbs
3,3631524
asked Jul 24 at 4:36
Samar Imam Zaidi
1,063316
2
Functions have domains and ranges, $x$ is an independent(ish) variable so I'm guessing $[0,pi]$ is the set of values you can plug into $x$, correct?
– Jacob Claassen
Jul 24 at 4:45
1
try graphing $y = cos x$ and $y = frac 80$ How many times within your domain of x do the curves intersect?
– Doug M
Jul 24 at 4:49
1
$cos(x)$ is strictly decreasing on the interval $[0, pi]$ whereas $displaystyle fracx80$ is strictly increasing. So if there is an intersection, there can be only one. The intermediate value theorem, if you're familiar with it, can help you conclude that an intersection does occur.
– Kaj Hansen
Jul 24 at 6:02
What does it mean that the range of $x$ is $[-80,80]$?
– Taroccoesbrocco
Jul 24 at 6:04
I think that the request is simply to find the number of all solutions. LHS and RHS are even fuctions so it’s enough to solve $cos x=x/80$ for positive $x$.
– Oldboy
Jul 24 at 6:05
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Find the number of solution of $cos x=fraclvert x rvert80$
Domain of $x$ is $[0,pi]$ and the range of $x$ is $[-80,80]$. I am not able to proceed.
trigonometry
edited Jul 24 at 6:59
Gibbs
3,3631524
asked Jul 24 at 4:36
Samar Imam Zaidi
1,063316
Find the number of solution of $cos x=fraclvert x rvert80$
Domain of $x$ is $[0,pi]$ and the range of $x$ is $[-80,80]$. I am not able to proceed.
trigonometry
edited Jul 24 at 6:59
Gibbs
3,3631524
asked Jul 24 at 4:36
Samar Imam Zaidi
1,063316
edited Jul 24 at 6:59
Gibbs
3,3631524
edited Jul 24 at 6:59
Gibbs
3,3631524
edited Jul 24 at 6:59
Gibbs
3,3631524
3,3631524
asked Jul 24 at 4:36
Samar Imam Zaidi
1,063316
asked Jul 24 at 4:36
Samar Imam Zaidi
1,063316
asked Jul 24 at 4:36
Samar Imam Zaidi
1,063316
1,063316
2
Functions have domains and ranges, $x$ is an independent(ish) variable so I'm guessing $[0,pi]$ is the set of values you can plug into $x$, correct?
– Jacob Claassen
Jul 24 at 4:45
1
try graphing $y = cos x$ and $y = frac 80$ How many times within your domain of x do the curves intersect?
– Doug M
Jul 24 at 4:49
1
$cos(x)$ is strictly decreasing on the interval $[0, pi]$ whereas $displaystyle fracx80$ is strictly increasing. So if there is an intersection, there can be only one. The intermediate value theorem, if you're familiar with it, can help you conclude that an intersection does occur.
– Kaj Hansen
Jul 24 at 6:02
What does it mean that the range of $x$ is $[-80,80]$?
– Taroccoesbrocco
Jul 24 at 6:04
I think that the request is simply to find the number of all solutions. LHS and RHS are even fuctions so it’s enough to solve $cos x=x/80$ for positive $x$.
– Oldboy
Jul 24 at 6:05
add a comment |Â
2
Functions have domains and ranges, $x$ is an independent(ish) variable so I'm guessing $[0,pi]$ is the set of values you can plug into $x$, correct?
– Jacob Claassen
Jul 24 at 4:45
1
try graphing $y = cos x$ and $y = frac 80$ How many times within your domain of x do the curves intersect?
– Doug M
Jul 24 at 4:49
1
$cos(x)$ is strictly decreasing on the interval $[0, pi]$ whereas $displaystyle fracx80$ is strictly increasing. So if there is an intersection, there can be only one. The intermediate value theorem, if you're familiar with it, can help you conclude that an intersection does occur.
– Kaj Hansen
Jul 24 at 6:02
What does it mean that the range of $x$ is $[-80,80]$?
– Taroccoesbrocco
Jul 24 at 6:04
I think that the request is simply to find the number of all solutions. LHS and RHS are even fuctions so it’s enough to solve $cos x=x/80$ for positive $x$.
– Oldboy
Jul 24 at 6:05
2
2
Functions have domains and ranges, $x$ is an independent(ish) variable so I'm guessing $[0,pi]$ is the set of values you can plug into $x$, correct?
– Jacob Claassen
Jul 24 at 4:45
Functions have domains and ranges, $x$ is an independent(ish) variable so I'm guessing $[0,pi]$ is the set of values you can plug into $x$, correct?
– Jacob Claassen
Jul 24 at 4:45
1
1
try graphing $y = cos x$ and $y = frac 80$ How many times within your domain of x do the curves intersect?
– Doug M
Jul 24 at 4:49
try graphing $y = cos x$ and $y = frac 80$ How many times within your domain of x do the curves intersect?
– Doug M
Jul 24 at 4:49
1
1
$cos(x)$ is strictly decreasing on the interval $[0, pi]$ whereas $displaystyle fracx80$ is strictly increasing. So if there is an intersection, there can be only one. The intermediate value theorem, if you're familiar with it, can help you conclude that an intersection does occur.
– Kaj Hansen
Jul 24 at 6:02
$cos(x)$ is strictly decreasing on the interval $[0, pi]$ whereas $displaystyle fracx80$ is strictly increasing. So if there is an intersection, there can be only one. The intermediate value theorem, if you're familiar with it, can help you conclude that an intersection does occur.
– Kaj Hansen
Jul 24 at 6:02
What does it mean that the range of $x$ is $[-80,80]$?
– Taroccoesbrocco
Jul 24 at 6:04
What does it mean that the range of $x$ is $[-80,80]$?
– Taroccoesbrocco
Jul 24 at 6:04
I think that the request is simply to find the number of all solutions. LHS and RHS are even fuctions so it’s enough to solve $cos x=x/80$ for positive $x$.
– Oldboy
Jul 24 at 6:05
I think that the request is simply to find the number of all solutions. LHS and RHS are even fuctions so it’s enough to solve $cos x=x/80$ for positive $x$.
– Oldboy
Jul 24 at 6:05
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
1
down vote
Calculate the number of full cosine "hills" from 0 to 80 (12). Each such hill gives two zeros. And you have one 'semi-hill' between 0 and $pi/2$. So the total number of zeros is 12$cdot$2+1=25 for $x>0$. Multiply this by 2 (because LHS and RHS a are symmetric with respect to $y$-axis) and you get 50 as the final answer.
answered Jul 24 at 6:20
Oldboy
2,6101316
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
Calculate the number of full cosine "hills" from 0 to 80 (12). Each such hill gives two zeros. And you have one 'semi-hill' between 0 and $pi/2$. So the total number of zeros is 12$cdot$2+1=25 for $x>0$. Multiply this by 2 (because LHS and RHS a are symmetric with respect to $y$-axis) and you get 50 as the final answer.
answered Jul 24 at 6:20
Oldboy
2,6101316
add a comment |Â
up vote
1
down vote
Calculate the number of full cosine "hills" from 0 to 80 (12). Each such hill gives two zeros. And you have one 'semi-hill' between 0 and $pi/2$. So the total number of zeros is 12$cdot$2+1=25 for $x>0$. Multiply this by 2 (because LHS and RHS a are symmetric with respect to $y$-axis) and you get 50 as the final answer.
answered Jul 24 at 6:20
Oldboy
2,6101316
add a comment |Â
up vote
1
down vote
up vote
1
down vote
Calculate the number of full cosine "hills" from 0 to 80 (12). Each such hill gives two zeros. And you have one 'semi-hill' between 0 and $pi/2$. So the total number of zeros is 12$cdot$2+1=25 for $x>0$. Multiply this by 2 (because LHS and RHS a are symmetric with respect to $y$-axis) and you get 50 as the final answer.
answered Jul 24 at 6:20
Oldboy
2,6101316
Calculate the number of full cosine "hills" from 0 to 80 (12). Each such hill gives two zeros. And you have one 'semi-hill' between 0 and $pi/2$. So the total number of zeros is 12$cdot$2+1=25 for $x>0$. Multiply this by 2 (because LHS and RHS a are symmetric with respect to $y$-axis) and you get 50 as the final answer.
answered Jul 24 at 6:20
Oldboy
2,6101316
edited Jul 24 at 9:04
answered Jul 24 at 6:20
Oldboy
2,6101316
answered Jul 24 at 6:20
Oldboy
2,6101316
answered Jul 24 at 6:20
Oldboy
2,6101316
2,6101316
add a comment |Â
add a comment |Â
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2
Functions have domains and ranges, $x$ is an independent(ish) variable so I'm guessing $[0,pi]$ is the set of values you can plug into $x$, correct?
– Jacob Claassen
Jul 24 at 4:45
1
try graphing $y = cos x$ and $y = frac 80$ How many times within your domain of x do the curves intersect?
– Doug M
Jul 24 at 4:49
1
$cos(x)$ is strictly decreasing on the interval $[0, pi]$ whereas $displaystyle fracx80$ is strictly increasing. So if there is an intersection, there can be only one. The intermediate value theorem, if you're familiar with it, can help you conclude that an intersection does occur.
– Kaj Hansen
Jul 24 at 6:02
What does it mean that the range of $x$ is $[-80,80]$?
– Taroccoesbrocco
Jul 24 at 6:04
I think that the request is simply to find the number of all solutions. LHS and RHS are even fuctions so it’s enough to solve $cos x=x/80$ for positive $x$.
– Oldboy
Jul 24 at 6:05